Quantum Master Equation Approach to Singlet Fission Dynamics in Pentacene Linear Aggregate Models: Size Dependences of Excitonic Coupling Effects

Abstract

The singlet fission (SF) dynamics of pentacene linear aggregate models are investigated using the quantum master equation method by focusing on the Frenkel excitonic (FE) coupling effects on the SF rate and double triplet (TT) yield as well as on their aggregate size dependences. It is found that for the dimer model, unrealistically large FE couplings are needed to provide significant effects on the SF dynamics, while for the larger aggregate models a realistic FE coupling causes significant variations in the SF dynamics: as increasing the aggregate size, the SF rate rapidly increases, attains the maximum at 8-mer (~3 times enhancement as compared to the non-FE-coupling case) and then decreases, approaching a stationary value after 12-mer, although the stationary TT yield at 20-mer remains slightly smaller than that in the non-FE-coupling case. These features are explained based on the relative relaxation factors between the adiabatic exciton states. The present results contribute to constructing the design guidelines for highly efficient SF aggregates. © 2018 Wiley Periodicals, Inc.

Theoretical Study on Singlet Fission Dynamics in Pentacene Ring‐Shaped Aggregate Models with Different Configurations

“…Although the point groups of linear aggregate N-mer belong to the C 2h or C 2v when N is odd or even, respectively, there is no problem whether we discuss the symmetry within the framework of the point group C 2 because of the symmetry of the HOMO and LUMO of pentacene molecule. In previously reported linear aggregate model, [34] which consists of three or more molecules, all the adiabatic FE' (TT') states including the lowest FE' state are found to be coupled with the diabatic TT (FE) states, and this linear aggregate model is found to belong to group II (Section VI in the Supporting Information). This is because the symmetry adapted TT states can have both irreducible representations A and B, where the irreducible representation A (B) is symmetric (antisymmetric) for the C 2 operation, due to the lack of interaction between the molecules at the ends of the aggregate.…”

“…In conclusion, we found i) that SF rate in H-type ring-shaped aggregate with odd N is found to be accelerated when the degenerate lowest FE' states approach to TT' manifold, and ii) that this condition for enhancing the SF rate is similar to that for linear aggregate N-mer (N^3) model, which belong to group II in the sense that the lowest FE' state include the TT configurations (see Figure S11 in the Support Information). [34] Next, we clarify the reason why H5 model in FE coupling case presents the largest SF rate (k = 8.48 ps À 1 ), which is~24 and~33 times as large as those in H3 (k = 0.352 ps À 1 ) and J5 (k = 0.260 ps À 1 ) models, respectively, and shows relatively high TT yield (a = 0.7798). As seen from the RRF analysis for H5 in FE coupling model (Figure 9), the degenerate FE'(a, b) states, which involve diabatic TT configurations, are close to neardegenerate TT' manifold, resulting in the large exciton overlaps of FE/TT configurations between FE'(a, b) and TT'(i, j) (see the exciton density in FE'(a) and TT'(i) in Figure 9).…”

“…Recently, the SF mechanism of linear and ring-shaped aggregate models has been investigated by Nakano et al in order to clarify how the size and periodical structure of molecular aggregates affect the SF rate and TT yield. [34,35] For example, it has been found that there exists an optimal aggregate size yielding the maximum SF rate. In the ring-shaped aggregate models, however, the variation in intermolecular electronic coupling depending on the size of aggregates has not been examined, though it is predicted to vary with aggregate size due to the change of relative configuration between the neighboring molecules.…”

“…The mechanism of the SF dynamics in the present ring-shaped aggregates is analyzed based on relative relaxation factor (RRF) analysis, which can clarify the primary SF pathways between adiabatic exciton states together with the origin of the relaxation rates. [29,34,35,42] Furthermore, we reveal the fundamental correlations between geometrical structure and SF efficiency more generally by examining the electronic couplings based on point group symmetry structures in ring-shaped aggregate models in comparison with the linear aggregate models. These results are expected to contribute to constructing more general and fundamental SF design guidelines for aggregate systems with various geometrical structures and size.…”

“…We calculate the intermolecular electronic coupling using the pentacene dimer unit as shown in Figure 1B with R = 3.7 Å and θ = 180°/N (in the J-aggregate) or 90°-180°/N (in the H-aggregate), where R indicates the intermolecular distance between the neighboring carbon atoms in the zigzag edges, and θ indicates the angle between the pentacene monomer plane and the longitudinal axis in parallel to the R direction. [34,35] As mentioned before, we evaluate the efficiency of SF by the rate and yields of generating correlated-triplet pair (TT). Note here that this is not the nature of rigorous quantum yields of SF process, that is, the yields of individual triplets after the separation of TT states.…”